We consider the problem of joint power allocation and distributed beamforming design for asynchronous two-way multi-relay networks, where two transceivers rely on an orthogonal frequency division multiplexing (OFDM) scheme to exchange information through multiple amplify-and-forward relay nodes. The network is assumed to be asynchronous in the sense that different relaying paths are subject to different propagation delays. This assumption renders the end-to-end channel between the two transceivers frequency-selective. The impulse response of such a channel can be modeled as a finite impulse response (FIR) system with multiple taps. We present a simple semi-closed-form solution for the problem of minimization of the total transmission power consumed in such networks subject to two quality of service constraints on the transceivers rates. We show that at the optimum, the end-to-end channel must be frequency-flat, which means only one tap of the end-to-end channel impulse response is non-zero. As a result, our semi-closed-form solution leads to a relay selection scheme, in which only those relays associated with the non-zero tap of the end-to-end channel impulse response are switched on, and the rest of the relays are kept off. The simulation results demonstrate that using the proposed semi-closed-form algorithm significantly outperforms the traditional best relay selection method.

中文翻译：

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多载波异步双向中继网络的功率优化分布式波束成形


我们考虑异步双向多中继网络的联合功率分配和分布式波束成形设计问题，其中两个收发器依靠正交频分复用（OFDM）方案通过多个放大转发中继节点交换信息。假设网络是异步的，因为不同的中继路径受到不同的传播延迟。这一假设使得两个收发器之间的端到端通道具有频率选择性。这种通道的脉冲响应可以建模为具有多个抽头的有限脉冲响应 (FIR) 系统。我们提出了一种简单的半封闭式解决方案，用于解决此类网络中消耗的总传输功率最小化的问题，该网络受到收发器速率的两个服务质量约束。我们证明，在最佳情况下，端到端信道必须是频率平坦的，这意味着端到端信道脉冲响应中只有一个抽头是非零的。因此，我们的半封闭式解决方案导致了一种继电器选择方案，其中仅那些与端到端信道脉冲响应的非零抽头相关联的继电器被打开，其余继电器被打开被关闭。仿真结果表明，使用所提出的半封闭式算法明显优于传统的最佳继电器选择方法。